# Set up an equation in the following cases:$(i)$. Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. [Take m to be the number of Parmit’s marbles.]$(ii)$. Laxmi’s father is 49 years old. He is 4 years older than three times Laxmi’s age. [Take Laxmi’s age to be y years.]$(iii)$. The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. [Take the lowest score to be l.]$(iv)$. In an isosceles triangle, the vertex angle is twice either base angle. [Let the base angle be b in degrees. Remember that the sum of angles of a triangle is 180 degrees].

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To do:

We have to set up an equation in the given cases.

Solution:

(i) Let Parmit have $m$ number of marbles

Then, Irfan has $(5m+7)$ marbles

Total number of marbles Irfan has $=37$

So, $5m+7=37$

(ii) Let the age of Laxmi be $y$ years

Laxmi’s father is four years older than three times Laxmi’s age.

Then Laxmi's father's age $=3y+4$ years

Also, the age of Laxmi’s father is 49 years.

According to the question, $3y+4=49$

(iii) Let the lowest marks obtained by the student be $l$

Then the highest marks obtained by the student is $2l+7$

And the highest score is $87$

Therefore, according to the question, $2l+7=87$

(iv) Let the base angle of a triangle be $b$.

Then the vertex angle of the isosceles triangle$=2b$.

According to the question, $b+b+2b=180^{\circ}$ [Since the sum of angles of a triangle is 180 degrees]

Thus, $4b=180^{\circ}$

Updated on 10-Oct-2022 13:33:38